The giant asset managers aim to push harder on the companies in which their index funds invest

Vanguard Group and BlackRock Inc., giant fund managers once known for quiet relationships with the companies in which they invest, say they are getting more assertive.

Vanguard is urging boards to be “substantially independent of management” and warns that it won’t sit idly by on corporate-governance issues, according to a letter from its chief executive sent to several hundred public companies over the past two days.